Decrement Of Vibrations Research Articles

The scientific landmarks for the development and evaluation of the effectiveness of vibration and noise absorbing materials

The mastic compositions with vibration and noise absorbing properties have been developed to reduce the level of noise and vibration in the low- and high-frequency range of the spectrum. Evaluation of the effectiveness of the developed vibration and noise absorbing mastic compositions “Vibroshtil” and “Vibroshtilmaxi” was carried out on an experimental installation by the method of free damping of plate vibrations with the determination of the decrement of vibrations. Mastic compositions are characterized by a high value of the sound absorption coefficient and the coefficient of mechanical losses in the range of operating speeds. The introduction of developed vibration and noise absorbing materials with an extended spectrum of action at the workplaces of workers will reduce the level of vibration and noise in the low- and high-frequency range of the spectrum by 7–15 dB and create safe working conditions. The main characteristic of the vibration and noise absorbing composite is the sound absorption coefficient, the value of which is in the range from 0 to 1. The main advantage of these compositions over the existing ones is the ease of manufacture, the ability to apply them to any surface by spraying or puttying.

MEANS OF INCREASING THE DYNAMIC QUALITY OF FINISHING AND BORING MACHINES

The article presents the design features of a number of spindle heads that ensure high accuracy of precision finishing and boring machines. The article describes the characteristics of the heads, spindle support devices, which increase the overall rigidity and damping of the spindle-bearing system. The basic designs of spindle heads, the relationships between design parameters are presented, and an analysis of their designs is also performed. Based on the processing of oscillograms of damped oscillations, the dependence of the logarithmic decrement of oscillations on their level was studied. Based on an experimental study of the characteristics of finishing and boring heads, the optimal values of the axial preload of the bearings were determined. It has been established that with increasing tension force, the oscillation decrement changes non-monotonically and has a maximum. This dependence is determined by the occurrence of linear resistance and dry friction forces in the dynamic system of the spindle assembly. Optimal tension values ensure maximum accuracy of the spindle assembly, and the temperature increase does not exceed 4...6°. We have found that creating a cavity at the free end of the console improves the dynamic quality of spindle assemblies with console tools. At the same time, the coefficients of dynamic disturbances in the spindle-boring bar system decrease. The work determines the influence of the cavity length on the coefficient of transfer of compensation from the front support to the cutter.Keywords: spindle head, bearing support, vibration decrement, rigidity, static and harmonic influence coefficients, tension forces

The Cold-Brittleness Regularities of Low-Activation Ferritic-Martensitic Steel EK-181

The behavior of the EK-181 low-activation ferritic-martensitic reactor steel (Fe–12Cr–2W–V–Ta–B) in the states with different levels of strength and plastic properties after traditional heat treatment (THT) and after high-temperature thermomechanical treatment (HTMT) in the temperature range from −196 to 25 °C, including the range of its cold brittleness (ductile–brittle transition temperature, DBTT) is studied. The investigations are carried out using non-destructive acoustic methods (internal friction, elasticity) and transmission and scanning electron microscopy methods. It is found that the curves of temperature dependence of internal friction (the vibration decrement) of EK-181 steel after THT and HTMT are similar to those of its impact strength. Below the ductile–brittle transition temperature, it is characterized by a low level of dislocation internal friction. The temperature dependence curves of the steel elastic modulus increase monotonically with the decreasing temperature. In this case, the value of Young’s modulus is structure-sensitive. A modification of the microstructure of EK-181 steel as a result of HTMT causes its elastic modulus to increase, compared to that after THT, over the entire temperature range under study. The electron microscopic studies of the steel microstructure evolution near the fracture surface of the impact samples (in the region of dynamic crack propagation) in the temperature range from −196 to 100 °C reveal the traces of plastic deformation (increased dislocation density, fragmentation of the martensitic structure) at all of the temperatures under study, including those below the cold brittleness threshold of EK-181 steel.

Влияние структурного состояния на упругие и микропластические свойства алюминиевого сплава AД1

The results of a study of aluminum alloy AD1 in four structural states before and after severe plastic deformation are presented. Both the initial coarse-grained state (supply state) and three fine-grained states, which differ from each other in the method of obtaining, are considered. Elastic and microplastic properties (modulus of elasticity, decrement of elastic vibrations, microplastic deformation) were determined by the acoustic method of a composite vibrator. It is shown that the modulus of elasticity changes to a large extent under the influence of the evolution of internal stresses; the attenuation of ultrasound after severe plastic deformation increases due to an increase in the area of grain boundaries. Key words: AD1 aluminum, modulus of elasticity, microcrystalline aluminum, decrement of elastic vibrations, microplastic deformation.

Improvement of the Dynamic Quality of Cantilever Boring Bars for Fine Boring

The paper presents ways to reduce the vibrations of special cantilever boring bars mounted on spindle heads of finishing and boring machines. Special cantilever boring bars are designed for machining holes in non-standard conditions, for example, when boring deep holes with l/d>3 (l–hole length, d-hole diameter) or holes with a discontinuous surface. The results of the experiments and theoretical developments, as well as the schemes of the experimental stands, are presented. The investigated methods for reducing fluctuations are the following: the use of a dynamic damper with intermittent cutting elements; the suppression of the normal vibrations of the cutter to the workpiece surface due to the excitation of vibrations directed tangentially to the workpiece surface and not causing processing errors; increased damping in the cutting zone when changing the design of the boring bar. The tuning parameters of the dynamic damper, the logarithmic decrement of vibrations, as well as the conditions for effective damping of vibrations during the interaction of their two coupled forms are given. The results are shown in the tables and graphs.

Damping analysis of stiffened laminated composite plates in thermal environment

High-strength and lightweight composites used in high-speed vehicles and aircraft experience increased temperature owing to aerodynamic friction. Because of the rise in temperature, the elastic moduli of the composites are degraded and inherent viscous damping is increased to the glass transition temperature. In this work, the damping performance of unstiffened and stiffened polyetheretherketone (PEEK) based intermediate modulus (IM7) carbon fiber laminated composite plates is evaluated at various temperatures using displacement- and energy-based approaches. In the displacement-based approach, the logarithmic decrement of the damped vibration is determined to investigate the effect of lamina sequences, stiffener orientation, and stiffener depth at different temperatures. A first-order shear deformation theory considering the viscoelastic property of the composite lamina is implemented to simulate the damped dynamic response of the laminated composite plates in a thermal environment. The best suitable damping model, among Rayleigh damping and modal expansion damping, has been identified to evaluate the damping matrix. Furthermore, the energy-based damping analysis appeared to be a robust approach to evaluate the damping performance as compared to the displacement-based analysis. It is concluded that stiffened plates effectively suppress the dynamic response at elevated temperature, whereas the unstiffened plates show relatively better damping performance at lower temperature.

Evaluation of the self-induced vibrations modes of bridge superstructure during monitoring

In the last 20–30 years, bridge condition monitoring during the operational cycle has become increasingly common on the Russian highway network. The monitoring ensures control of the bridge on an ongoing basis in a continuous mode. The task facing the monitoring systems developers is to expand the range of the parameters that can be used in real-time to monitor the bridge’s condition and the safe conditions for its operation. One way is to use indirect parameters obtained as a direct data processing result. Appropriate algorithms for converting information recorded by the system sensors and obtaining new parameters are needed. The most important design characteristics are dynamic characteristics, which include the frequencies and amplitudes of the self-induced vibration modes, and vibration decrements. This article discusses a technique for estimating the dynamic bridge characteristics, namely, the self-induced vibration modes frequencies and amplitudes using experimental data. A dynamic system mathematical model that performs self-induced vibration is considered in the system form with one input signal and n output signals. Formulas for the model frequency response and its components are given: the amplitude and phase response of the system. To calculate the frequency response, power spectra and cross-power spectra are needed, which are obtained using the Fourier transforms of the signal. The article shows how, to reduce the random error, to estimate the mutual spectrum by dividing the realizations into several adjacent intervals (segments) of length T each. The final spectrum (periodogram) is obtained as the arithmetic mean of the segment spectra. Monitoring systems using accelerometers that measure the structure linear accelerations of the record the output signals. One of the accelerometers is considered an input signal source. According to the proposed mathematical model, the self-induced vibration frequency response of the system characterizes the amplitudes and signs of the structure displacements at the accelerometers’ location at different frequencies. The mathematical apparatus considered by the authors is applied to the data obtained on a real object: a bridge crossing over the Volga river on the highway Nizhny Novgorod-Shakhunya-Kirov in the Nizhny Novgorod region — Borsky Bridge. The monitoring of the bridge state stream crossing the Volga by its purpose is control and research, in terms of the form of information presentation over time — continuous, in terms of the speed and synchronism of polling sensors — dynamic. The monitoring purpose is to monitor the bridge structure operation and its operating conditions, including the technical control of the stress-strain state (SSS) parameters. The bridge characteristics and the current monitoring system are given. The results of numerical calculations of the arch span for vibrations are presented. The authors performed periodogram calculations using the mathematical package MathCad using the signals of two accelerometers. To estimate the frequencies and amplitudes of the span structure vibration modes using monitoring data, periodogram calculations were performed using the SpektrKatKross program that implements the proposed algorithm. The correspondence results of the program to the results of the calculations by the program MathCad are shown. The calculated and experimental vibration modes of the span are close. As a result of using the proposed mathematical model, the reliability of this comparison is ensured both in terms of frequencies and in terms of amplitudes.

ДОСЛІДЖЕННЯ ВПЛИВУ ПІДВИЩЕНОЇ ТЕМПЕРАТУРИ НА ДИСИПАТИВНІ ВЛАСТИВОСТІ ОДНОСПРЯМОВАНОГО ВУГЛЕПЛАСТИКУ

An experimental method for determination of composite materials dissipative properties, the main characteristic of which is the minimization of external energy losses and ensuring uniform distribution of deformations along the specimen working part under the pure bending condition has been developed. The scheme of the modernized experimental setup is presented. Its mechanical system represents a closed circuit in which the energy in material specimen under flexural vibrations is dissipated. Automated testing and registration of vibration characteristics were carried out by the method of attenuating vibrations at different temperatures. Based on the results for a set of experimental studies on the determination of the dissipative properties of unidirectional CFRP specimens under the pure bending conditions, the dependencies of the logarithmic decrement of vibrations on the relativedeformation in the range (2...12)∙10–4for temperatures from 300 K to 423 K was established.To analyze the effect of temperature on the dissipative properties of the composite, a parameter is proposed that is determined by the increment of the logarithmic decrement of vibrations (LDV) before deformation. It is shown that it is a more informative indicator of the structural integrity of carbon fiber samples, even with a relatively small violation of it due to heating and simultaneous cyclic deformation, compared to the relative growth of the LDV and the drop in the vibration frequency.The obtained experimental data and the presented method of investigation the dissipative properties of materials can be used as a directory data in the design of new models of equipment and in the development of mathematical models of composite structural elements operating under dynamic loads and elevated temperatures.

Flexural vibrations of the console with frictio

An approximate approach is considered for determining the logarithmic decrement of Flexural vibrations of an elastic console with a load at the end. The method proposed in Postnikov V. S.’s monograph on internal friction in metal is used. In this problem statement, the friction is assumed to be small. Therefore, the forms of natural vibrations of the console with friction are considered equal to the forms of natural vibrations of the console without friction. An approximate solution of this problem is obtained using a frequency experiment.

Radiation hardening and optical properties of materials based on SiO2

Preliminary studies have shown that the optical absorption spectra of radiation-colored glasses correspond to the spectral behavior of the scattering losses of an optically inhomogeneous medium. The reasons for the same optical changes in glasses of different compositions are the radiation-induced electric charge separation in the structurally nano-inhomogeneous glass volume, polarization and formation of nanometer optical inhomogeneities. The authors of this work prove that the radiation changes in the mechanical and optical properties of silicate glasses are of the same nature. The performed estimates indicate that the electric charge separation in the glasses occurs up to absorbed doses of about 1 MGy. The local electric charge separation due to the appearance of Coulomb forces leads to radiation hardening of the glasses. The estimated Coulomb hardening of the quartz glasses was ~ 107 Pa. The theoretical results were experimentally confirmed by measuring the mechanical properties of the glasses under high intensity proton irradiation as well as by testing the mechanical strength of a composite material based on quartz glass. Under proton irradiation with a dose rate of 5×103 Gy/s (energy of 8 MeV) up to threshold doses of ~ (1 – 5) ×106 Gy in the KU-1 quartz glasses, the decrement of acoustic vibrations decreased due to Coulomb hardening. After gamma irradiation with 1.34×105 Gy, the tensile strength of the composite material based on quartz glass increased by up to 20 MPa. This value is in the range of estimates of Coulomb hardening of quartz glasses. It is also shown that ionizing radiation does not affect the elastic modulus of materials based on SiO2.

Oscillations of Slabs Supported on Point Supports

The urgent task which is addressed in this work is the development of methods for determining the frequencies and forms of vibrations, as well as dynamic reactions of thin slabs with various support systems, including those supported on point supports.The aim of the work is to develop experimental methods for determining the frequencies and forms of natural oscillations of slabs with holes and thin point-supported square solid ones.In this work, the frequencies of square slabs with free edges resting on point supports are determined; the dependences of the vibration frequencies of slabs from the coordinates of point supports and the dimensions of symmetrically placed holes; the arrangement of point supports, wherein the basic frequency of free vibrations of the slab is maximum; the frequencies, shapes, and decrements of vibrations of square slabs supported on four point supports were determined experimentally, as well as the influence of the presence of holes and the degree of pinching of the supports on the dynamic characteristics of these slabs.The article deals with the method and analysis of results of experimental investigations of dynamic characteristics of square solid slabs with holes.Comparison of experimental and theoretical values of frequencies of natural oscillations of slabs showed their good similarity.The results of this work can be applied to dynamic and seismic calculations of point-supported square slabs.

ОПРЕДЕЛЕНИЕ ЛОГАРИФМИЧЕСКОГО ДЕКРЕМЕНТА КОЛЕБАНИЙ ЗДАНИЙ И СООРУЖЕНИЙ

Abstract. For the passport of buildings and structures, it is required to determine the logarithmic damping decrement. The proposed expressions [1, 2] to determine the decrement use the value of the Q-factor, however, an expression is known in which the damping decrement is determined through the logarithm of the ratio of the amplitudes of the damped signal. Comparison of the formulas for calculating the logarithmic decrement of vibrations was carried out using the example of data obtained when testing a beam with reinforcement.

Идентификация релаксационных максимумов внутреннего трения в сплаве Zr – Nb после азотирования, окисления на воздухе и науглероживания in situ

The internal friction method was used to study the behavior of the Zr – 1 wt. % Nb alloy after oxidation in air, nitriding in an atmosphere of technical nitrogen, and in situ carburization during measurements. In this case, carbon was deposited on the samples during measurements due to thermal decomposition of vapors of diffusion oil. The pressure in the system was about 10–2 Pa. The temperature dependence of the logarithmic decrement of damped bending vibrations with a frequency of 2.2 – 2.4 Hz was measured on specimens in the form of a rectangular plate 22 × 8 × 0.3 mm in size. The measurements were carried out at a constant heating rate of about 4 K/min from room temperature to 700 – 750 °C. The obtained temperature dependences of internal friction were divided into partial maxima using a special program. The program determines the temperatures of the relaxation maxima and calculates the effective activation energy using the Werth — Marx formula. The internal friction spectra in successive measurements on one sample changed due to the diffusion redistribution of the alloy components. The parameters of the relaxation maxima for carbon (153 – 159 kJ/mol), oxygen (203 – 207 kJ/mol) and nitrogen (235 – 238 kJ/mol) in the alloy under study, depending on the experimental conditions, have been established. Grain-boundary (Gb) impurity maxima due to these impurities were also found. The following activation energies were obtained: 173 – 179 kJ/mol for C-Gb, 216 – 219 kJ/mol for O-Gb and 222 – 229 kJ/mol for N-Gb. Impurity grain-boundary maxima associated with carbon, oxygen, and nitrogen were observed in each series of measurements. The activation energy of the grain-boundary maxima proper decreases monotonically from 202.4 to 194.5 kJ/mol in a series with oxidation in air (experiments 711 – 715), and remains about 200 kJ/mol in nitrided samples.

Analysis of free vibrations of sandwich panel with electrorheological layer based on two models of laminated shells

Based on two models of laminated shells, free low frequency vibrations of a three-layered cylindrical panel with the internal layer fabricated of an electrorheological composite are studied. Both models lead to the same governing equations accounting for shears in layers, but differ in equations for calculating the reduced shear parameter which depends on the electric field strength and the temperature of a composite. In the case of a simple support of all edges, the formula for the complex natural frequency is obtained explicitly. The influence of the electric field strength and the temperature of the electrorheological composite on the lowest natural frequencies and associated vibration decrements is investigated. It was detected that both models give very close results for the heated composite at an electric field strength of more than 1.5 kV/mm. It is also shown that the frequency of natural vibrations of the electrorheological panel is a monotonically increasing function of the electric field strength, while the decrement – strength curve shows the presence of a local maximum corresponding to the best damping of viscoelastic vibrations.

Active Damping of Nonstationary Vibrations of a Three-Layer Electro-Viscoelastic Composite Plate

A method for constructing nonstationary vibration equations for electro-viscoelastic composite plates with their active damping is described. The problem is solved in an integral Fourier transform frequency space. To construct a multilayer plate model, a discrete structural approach was used, i.e., the plate is divided through the thickness into computational layers, within which the displacements and electric potentials are approximated by means of quadratic Lagrange polynomials. At the edges of the plate, the Navier conditions are met. The semi-analytical nonstationary vibration equations are derived by means of the variational convolutional Lagrange equation. To represent them in a frequency space, a direct integral Fourier transform is used, which makes it possible to use experimentally determined frequency-dependent complex characteristics directly in calculations of nonstationary vibrations of plates without additional transformations of integral physical relations. Solutions of the problem of active damping of nonstationary vibrations for the frequency images of displacements and electric potentials have been found, their convergence is analyzed. The procedure has been evaluated by analyzing the active damping of nonstationary vibrations of a three-layer edge-hinged square plate under the action of a blast wave impulse. The middle layer is made of a composite material, and the outer electro-viscoelastic layers act as a sensor and an actuator. The active damping of vibrations is provided by connecting these layers of the plate into a negative feedback circuit with the proportional-differential control law. The viscoelastic and electro-viscoelastic characteristics of the materials are taken into account by means of complex elastic, dielectric and piezoelectric moduli. The results of analyzing the active damping of nonstationary vibrations of a plate are presented. The values of the proportional and differential components of the controller as characteristics of this damping were chosen taking into account the permissible electric field strength of the actuator. The research results for the case of passive damping of vibrations are also given for comparison. The dependences of the decrement of plate vibrations on the differential component of the controller and of the maximum plate deflection on the reinforcement angle of the middle layer material have been established. The optimum reinforcement angle according to the minimum plate deflection criterion has been determined, which provides an increase in the efficiency of active damping of nonstationary vibrations of the plate owing to an increase in the differential component of the controller.

To the Construction of the Amplitude Dependence of Internal Friction with Vibrations of Porous Metal Composites

Purpose of research was to plot the amplitude dependence of the decrement of longitudinal and bending vibrations of samples of porous metal composites manufactured using 3D technology.Methods. The main attention is paid to the role of microplasticity in the scattering of the vibration energy, since the decrement value in composite will be greater than in monolithic material. The effect of porosity on the level of energy dissipation is taken into account. We have used a statistical model based on the results of the theory of functionals given on random processes.Results. This made it possible to find the concentration of microplastic zones in the composite during longitudinal and bending vibrations of the sample. The value of the vibration decrement is defined as the ratio of the potential energy of plastic deformations to the total potential energy of the entire sample. To calculate the effective moduli in the composite, the well-known technique of the theory of elasticity of micro-inhomogeneous media is used. The results obtained indicate that porosity significantly affects the concentration of microplastic zones and the scattering of internal friction during longitudinal and bending vibrations. However, it should be noted that at low amplitudes, microplastic regions are not formed in the vicinity of the pores. Therefore, the reasons for the appearance of energy dissipation are not explained only by microplasticity. The source of such losses are dislocation, ferromagnetic and other reasons. However, the level of these losses is much less than that indicated in this work, and depends only on the oscillation frequency.Conclusion. The results obtained can be used to establish the patterns of behavior of various natures of ingot, powder and composite materials with high dispersion in phase and structural components in various conditions and states.

Graphic method for assessing the margins of resistance to acoustic vibrations in the chambers of rocket engines by combustion noise

An experimental method is proposed for estimating the damping decrements of pressure fluctuations in the combustion chambers of forced rocket engines. The method is based on the statistical processing of noise pressure pulsations in the vicinity of natural resonance frequencies for normal modes of acoustic vibrations of the reaction volume and the subsequent prediction of the instability of the combustion process relative to acoustic vibrations. Based on the theory of statistical regression for multidimensional experimental data, the problem of predicting unknown parameters of sample distributions is solved by asymptotic determination of the correlation coefficient of the damping decrement of pressure vibrations through optimal linear predictors and the Kolmogorov distribution. Keywords rocket engine, combustion chamber, acoustic vibrations, combustion noise, spectral characteristics, Kolmogorov criterion, damping decrement. KniaZ988@mail.ru

Effective Reduction of Cyclic Stresses in Coated Samples

Two condensed electron-beam copper coatings, one consisting of copper and the other of Hf/Ag/Ni/Cr microlayers, were deposited onto a titanium alloy (Ti−6Al−4V) substrate to study the energy dissipation and fatigue resistance in the uncoated and coated samples under nonbreaking and breaking cyclic stresses. The microlayer coating is peculiar in that a material with a higher elastic modulus is used in each subsequent layer (from the substrate to the outer layer) and the coating layers and submicron twins in the binder sublayer have a columnar microstructure peculiar to electron-beam evaporation and vacuum condensation. Having layered macro- and microstructure, the coating absorbs the energy of vibrations through both internal friction (between the coating layers and between the coating and substrate) and dissipation of vibration energy on numerous defects in the columnar structure (intercolumnar porosity). Resonant first- and secondmode vibrations were excited in cantilevered samples to determine how the vibration decrement depended on their maximum stresses and the breaking fatigue stresses on the number of load cycles. In addition, vibration transmission coefficients for cyclic stresses and vibration energy were experimentally defined and justified for use. One coefficient is equal to the ratio of difference in stresses between the uncoated and coated samples to stresses in the uncoated sample, relative machine power being the same in various tests. The other coefficient is equal to the ratio of difference in energy between the uncoated and coated samples to the energy of vibrations induced in the uncoated sample, relative machine power being the same in various tests. The Hf/Ag/Ni/Cr coating is shown to provide greater energy dissipation but lower fatigue properties than the Cu coating and substrate. The vibration transmission coefficients are more sensitive to energy dissipation than the vibration decrement is.

Numerical Modeling of Resonant Vibrations of an Elongate Plate with an Integral Damping Coating

The classical methods of surface damping of bending vibrations of thin-walled structures and a promising integrated version with a damping coating consisting of two layers of a material with pronounced viscoelastic properties and an intermediate thin reinforcing layer of a high-modulus material are discussed. A four-layer finite element for an elongate plate with an integral damping coating is developed taking into account the lateral compression of the damping layers. A system of governing equations of the finite-element method is constructed for analyzing the dynamic response of the plate during its resonant vibrations. Iterative algorithms have been developed to take into account the amplitude dependence of the logarithmic decrements of vibrations of material of the damping layers when determining the damping properties of the plate and determining its vibration eigenmodes and eigenfrequencies with consideration of frequency dependence of the dynamic elastic moduli of the material. Numerical experiments were carried out to test the finite element developed and the iterative algorithms mentioned. The influence of aerodynamic resistance forces on the overall damping level of a cantilever plate with an integral damping coating is assessed.

Experimental investigation of natural and harmonic vibrations of plates interacting with air and fluid

The paper presents the results of the study of natural frequencies and the corresponding decrements of harmonic vibrations of rectangular plates located in air or on the free surface of the fluid. Using a specially designed experimental setup, the excitation of vibrations was carried out by the electromagnetic field. The measurements were taken with a Polytec PDV-100 digital laser vibrometer. The locations of points on the surface of the plates, at which an electromagnetic force was applied and the vibration velocity was measured, were determined from the solution of the modal problem by the finite element method. The decrements of plate vibrations were experimentally found for different schemes of plate clamping, and dependences of decrements on the amplitude were determined. It was found that the decrement corresponding to one mode of vibration (bending or torsional) increases with an increase in the number of nodal lines. The obtained results showed that during the interaction of the plate with the fluid, this relationship could be disturbed sometimes.